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@ARTICLE{Hijar:1884,
      author       = {Hijar, H. and Quintana, J. and Sutmann, G.},
      title        = {{P}robability distributions of {H}amiltonian changes in
                      linear magnetic systems under discontinuous perturbations},
      journal      = {Journal of statistical mechanics: theory and experiment},
      issn         = {1742-5468},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {PreJuSER-1884},
      pages        = {P05009},
      year         = {2008},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {A model for the stochastic evolution of a linear
                      paramagnetic system in contact with a thermal bath and
                      subjected to variations in time of an external magnetic
                      field, H, is presented. Changes in the Hamiltonian of this
                      system, H-H, defined through the relation (W) over tilde =
                      integral dH (partial derivative H-H/partial derivative H),
                      are considered for the special case in which the external
                      field is varied from an initial to a final value in
                      discontinuous successive steps. Distribution functions of W,
                      P-F((W) over tilde) and P-R((W) over tilde), corresponding
                      to switching on and switching off processes, respectively,
                      are explicitly calculated. To study the relaxation process,
                      it is assumed that in between successive variations of the
                      external field, the system follows a linear Langevin
                      dynamics in the presence of a constant field. The
                      dependences of P-F((W) over tilde) and P-R((W) over tilde)
                      on the number of steps in which the external field changes
                      from initial to final values as well as on the time rate of
                      the processes are presented. These distributions are used to
                      estimate free energy differences between two equilibrium
                      states via the relations of Jarzynski and Crooks, and it is
                      verified that these relations yield correct estimations of
                      the free energy difference. Results of the model are
                      illustrated firstly, for a system of independent two-level
                      spins in the thermodynamic limit. Finally, a comparison is
                      also performed with distributions of (W) over tilde in the
                      two-dimensional Ising model obtained independently from
                      numerical simulations, carried out in the paramagnetic phase
                      and restricted to perturbations that produce a linear
                      response. A good agreement is found between simulations and
                      the present calculations.},
      keywords     = {J (WoSType)},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {Scientific Computing},
      pid          = {G:(DE-Juel1)FUEK411},
      shelfmark    = {Mechanics / Physics, Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000256454900009},
      doi          = {10.1088/1742-5468/2008/05/P05009},
      url          = {https://juser.fz-juelich.de/record/1884},
}